I would add that adjective to agree with this sentence. Humans are agents, but they aren't rational.

If your reread the sentence you may note that I was careful to make that adjective redundant - sufficiently redundant as to border on absurd. "A rational agent will X or be irrational" is just silly. "A rational agent will X" would have been true but misses the point when talking about humans. That's why I chose to write "An agent will X or be irrational".

Yes. Unless being cooperative makes more Cooperative bots (and not more defecting bots) than defecting makes rational bots (and not Cooperative bots)

No. Cooperating is different to being a Cooperate-Bot. A rational agent will cooperate when it will create a better outcome via, for example, making other people cooperate. A Cooperate-Bot will cooperate even when it creates bad outcomes and completely independently of the responses of other agents or their environment. The only situations where it can be expected for it to be better to be a Cooperate-Bot than a rational agent that chooses to cooperate are those contrived scenarios where an entity or the environment is specifically constructed to read the mind and motives of the agent and punish it for cooperating for rational reasons.

I don't understand why you have gone through my various comments here to argue with trivially true statements. I was under the impression that I mostly joined the conversation agreeing with you.

A rational agent among irrational agents can actually be better off helping them cooperate and coordinate to avoid a specific situation in certain conditions rather than just plain old defecting.

Yes. When an agent can influence the behavior of other agents and cooperating in order to do so is of sufficient benefit it will cooperate in order to influence others. If this wasn't the case we wouldn't bother considering most of the game theoretic scenarios that we construct.